PSI - Issue 54

Francisco Q. de Melo et al. / Procedia Structural Integrity 54 (2024) 585–592 Author name / Structural Integrity Procedia 00 (2019) 000 – 000 ( ) = (1 – /( )) = ℎ × ( /2) × (1 – /( )) ,

590

6

(10)

with Î(0, ).

a)

b)

Figure 3: a) effect of tensile force in a side edge cracked plate and b) pure bending of the edge cracked plate

3. Evaluation of flexibility factors using Mohr’s integrals (method of areas) 3.1. Extensional mode load: displacement of both faces at the crack plane A specific bending moment also rotates the cracked plate at the crack tip and extends the distance between points of moment application. By using the Mohr’s integral as an approach to evaluate flexibility factors after applying a specific extensional force or a specific bending moment . In case of flexibility factor , the bending moment diagram , due to a unitary force = ; = , as depicted in Figure 2 , is combined with its own diagram. Expressions are as follows: 11 = 1 ∫ ( ) × ( ) ( ) = 0 11 = 1 ∫ (ℎ−( 6 − )) 3 ( − ) 2 0 = 6 [ 3 2 2(ℎ−−2 ℎ ) 2 + ( ℎ− ℎ )] , (11) Previous expression for 11 must be updated for the extension displacement due to force = ℎ . The section varies linearly with coordinate ; then: 11 = 1 ∫ 1 × 1 ( ) 0 11 = 1 ∫ (ℎ − ( − )) 0 = (ℎ −ℎ ) (12) Finally, for a unitary force 1 = 1 = ℎ , once we are only computing the mutual displacement/rotation of both faces of the edge crack opening, it is necessary to remove the displacement due to the entire “no - crack” (that is, with a solid uniform section) tensioned plate limited between two extreme nodes at distance :